The nuclei of atoms that have a magnetic moment will have sharply defined frequencies of nuclear oscillation in a strong magnetic field (Larmor frequency). The frequency of oscillation of each atomic nucleus will depend on its mass, its dipole moment, the chemical bonding of the atom, the atom's environment (which will be affected by electromagnetic coupling to other atoms in the vicinity), and the strength of the magnetic field seen by the atom. Thus, the frequency of oscillation will be characteristic, not only of the various atomic species, but also of their molecular environments. By resonantly exciting these oscillations, the atomic species and their environments can be determined with accuracy. This phenomenon is known as “nuclear magnetic resonance,” or NMR.
If a pulse of RF energy is applied at a resonance frequency of atoms of a particular species and environment (e.g. hydrogen atoms in a water environment), the atomic nuclei of this type and environment will resonantly be excited, and will later make a transition back to a low state of excitation. This transition is accompanied by emission of a radio-frequency signal, at the excitation frequency or a known lower frequency. The signal is known as the Free Induction Decay (FID) The amplitude and the shape of this FID-curve is related to the amount of nuclei involved in the process and to specific conditions and properties of the atoms in relation to the environment.
The use of NMR techniques in measurement, detection and imaging has become desirable in many scientific fields of endeavor. The non-invasive, non-destructive nature of NMR has facilitated application to industrial instrumentation, analysis and control tasks.
Almost every element in the periodic table has an isotope with a non-zero nuclear spin. This spin causes the nuclei to be magnetically active. Among magnetically active nuclei, NMR can only be performed on isotopes whose natural abundance is high enough to be detected. Commonly encountered magnetically active nuclei are 1H, 13C, 19F, 23Na, and 31P. The most common is 1H, which also possesses the largest magnetic moment, rendering it most advantageous for the performance of NMR spectroscopy.
Upon application to a sample of a static magnetic field, Bo, sample nuclear spins align with the field, parallel to the direction of the field. The magnetic moments can align themselves either parallel (NSNS) or antiparallel (NNSS) to the static field. Alignment parallel to the static field is the lower energy state and alignment against the field is the higher energy state. At room temperature, the number of nuclei having spins in the lower energy level, N+, slightly outnumbers the number in the upper level, N−. Boltzmann statistics provides thatN−/N+=exp(−E/kT),  (1)where E is the energy difference between the spin states; k is Boltzmann's constant, 1.3805×10−23 J/Kelvin; and T is the temperature in Kelvin. As the temperature decreases, so does the ratio N−/N+. As the temperature increases, the ratio approaches unity.
Owing to the slight imbalance of nuclei having spins at the higher state, a sample in a static magnetic field will exhibit a magnetization parallel to the static field. Magnetization results from nuclear precession (relaxation) around the static magnetic field. The frequency of this precession depends on the strength of the static magnetic field, and is defined as:v=γB,  (2)where B is the magnetic field strength and Gamma is the gyromagnetic ratio of at least one atom, typically hydrogen, in the sample material. The gyromagnetic ratio is related to the magnetic moment of the nucleus under analysis. The gyromagnetic ratio of protons is 42.57 MHz/Tesla. The frequency thus measured is known as the Larmor frequency, v, which can be conceptualized as the rate of precession of the nucleus in the static magnetic field or the frequency corresponding to the energy at which a transition between the upper and lower states can take place.
The fundamental NMR signal is derived by inducing transitions between these different alignments. Such transitions can be induced by exposing a sample to the magnetic component of an RF (radio frequency) signal, typically generated by an RF coil. When the magnetic component is applied perpendicularly to the magnetic field a resonance occurs at a particular RF frequency (identical to the precession frequency, the Larmor frequency), corresponding to the energy emitted or absorbed during a transition between the different alignments. When a strong magnetic field, such as in the range of 0.1–2 Tesla (1 T=10,000 Gauss) is used, this resonance typically occurs in the megahertz frequency range, corresponding to FM radio. Hence the radiation is known as Radio Frequency (RF) radiation.
The signal in NMR spectroscopy results from the difference between the energy absorbed by the spins which make a transition from the lower energy state to the higher energy state, and the energy emitted by the spins which simultaneously make a transition from the higher energy state to the lower energy state. The signal is thus proportional to the population difference between the states. NMR spectroscopy gains its high level of sensitivity since it is capable of detecting these very small population differences. It is the resonance, or exchange of energy at a specific frequency between the spins and the spectrometer, which gives NMR its sensitivity.
Pulsed NMR spectroscopy is a technique involving a magnetic burst or pulse, which is designed to excite the nuclei of a particular nuclear species of a sample being measured after the protons of such sample have first been brought into phase in an essentially static magnetic field; in other words the precession is modified by the pulse. Typically, the direction of the static magnetic field, Bo, is thought of as being along the Z-axis in three-dimensional space. At equilibrium, the net magnetization vector lies along the direction of the applied magnetic field Bo and is called the equilibrium magnetization Mo. In this configuration, the Z component of magnetization MZ equals Mo. MZ is referred to as the longitudinal magnetization. There is no transverse (MX or MY) magnetization in such a case.
It is possible to change the net magnetization by exposing the nuclear spin system to energy of a frequency equal to the energy difference between the spin states. If enough energy is put into the system, it is possible to saturate the spin system and make MZ=0. The time constant, which describes how MZ returns to its equilibrium value, is called the spin lattice relaxation time (T1). The equation governing this behavior as a function of the time t after its displacement is:MZ=M0 (1−e−t/T1)  (3)T1 is therefore defined as the time required to change the Z component of magnetization by a factor of e. Hence, at t=T1, MZ=0.63 M0. In order to properly perform repeated measurements, which is necessary in order to reduce background noise and enhance signal quality, M0 should be allowed to return to MZ. In other words, the longitudinal magnetization MZ, which equals zero upon saturation, should be allowed to fully return to the +Z direction and attain its equilibrium value of M0. While this theoretically would take forever, (i.e., following saturation, MZ=M0 when t=∞), it is generally considered sufficient when MZ=0.99 M0, which occurs when t=5T1. This places time constraints on the speed at which a sample may be measured multiple times or the overall throughput of samples through an interrogation zone.
If the spin system is oversaturated, forcing the net magnetization into the −Z direction, it will gradually return to its equilibrium position along the +Z axis at a rate also governed by T1. The equation governing this behavior as a function of the time t after its displacement is:Mz=M0 (1–2e−t/T1)  (4)The spin-lattice relaxation time (T1) is the time to reduce the difference between the longitudinal magnetization (MZ) and its equilibrium value by a factor of e. Here, too, an elapsed time of t=5 T1 is required in order for MZ to return to a value of 0.99 MO, placing a similar time constraint on sample throughput.
If the net magnetization is rotated into the XY plane by a 90° pulse, it will rotate about the Z-axis at a frequency equal to the frequency of a photon, having the energy corresponding to a transition between the two energy levels of the spin. This frequency is called the Larmor frequency. In addition to the rotation, the net magnetization, now in the XY plane, starts to dephase because each of the spin packets making it up is experiencing a slightly different magnetic field and hence rotates at its own Larmor frequency. The longer the elapsed time, following the pulse, the greater the phase difference. If the detector coil is sensitive to measurements of fields in the X-direction alone, the dephasing results in a decaying signal, eventually approaching zero. The time constant, which describes this decay of the transverse magnetization, MXY, is called the spin-spin relaxation time, T2.MXY=MXY0e−t/T2  (5)T2 is always less than or equal to T1. The net magnetization in the XY plane goes to zero and then the longitudinal magnetization grows until Mo returns to the +Z direction. Any transverse magnetization behaves the same way.
The spin-spin relaxation time, T2, is the time to reduce the transverse magnetization by a factor of e. The difference between spin-lattice relaxation and spin-spin relaxation is that the former works to return Mz to M0, while the latter works to return Mxy to zero. T1 and T2 were discussed separately above, for clarity. That is, the magnetization vectors are considered to fill the XY plane completely before growing back up along the Z-axis. Actually, both processes occur simultaneously, with the only restriction being that T2 is less than or equal to T1.
Two factors contribute to the decay of transverse magnetization—(1) molecular interactions (said to lead to a pure T2 molecular effect), and (2) variations in Bo (the applied static field), said to lead to an inhomogeneous T2 effect. The combination of these two factors is what actually results in the decay of transverse magnetization. The combined time constant is called “T2 star” and is given the symbol T2*. The relationship between the T2 from molecular processes and that from inhomogeneities in the magnetic field is1/T2*=1/T2+1/T2inh.  (6)The source of the inhomogeneities can be natural fluctuations in a field, or imperfections in the magnets generating the field or magnetic contaminants, such as iron or other ferromagnetic metals.
In practice, to actually measure a sample using NMR, a sample is first placed in a static magnetic field, Bo, which is the interrogation zone of the instrument. Next, a magnetic pulse is applied, which rotates the magnetization vector to a desired extent, typically 90° or 180°. A 90° pulse, for example, rotates the magnetization vector from the Z-direction into the XY plane resulting in transverse magnetization, MXY, as discussed above. After the application of the pulse, there occurs a free induction decay (FID) of the magnetization associated with the excited nuclei.
Traditional Fourier Transform analysis transforms a time domain spectrum (amplitude of magnetization vectors vs. time) into a frequency domain spectrum (frequency vs. relative amplitude), which separates individual frequencies out of a multiphase spectrum. This separation can be used to advantage in studying the nuclei of interest. The duration of the pulses, the time between the pulses, the pulse phase angle and the composition of the sample are parameters, which affect the sensitivity of this technique.
International Patent Application No. WO9967606, incorporated herein by reference as if fully written out below, describes a check weighing system for samples on a production line, including a magnet for creating a static magnetic field over an interrogation zone to create a net magnetization within a sample located within the interrogation zone, and an RF coil for applying an alternating magnetic field over the interrogation zone to cause excitation of the sample according to the principles of NMR.
The use of NMR for techniques for check weighing samples on a production line encounters a variety of difficulties, including but not limited to the presence of interfering species such as metal particles either within the sample container or elsewhere in the system, effects of temperature on the magnet or electronics, humidity in the sample or system, and mechanical instability of the containers.
It would be desirable to provide a system and method for identifying and/or compensating for the above noted potential sources of imprecise measurements for an NMR sample check weighing system.